Pré-Publication, Document De Travail Année : 2025

Identifying the Best Transition Law

Résumé

Motivated by recursive learning in Markov Decision Processes, this paper studies best-arm identification in bandit problems where each arm's reward is drawn from a multinomial distribution with a known support. We compare the performance reached by strategies including notably LUCB without and with use of this knowledge. In the first case, we use classical non-parametric approaches for the confidence intervals. In the second case, where a probability distribution is to be estimated, we first use classical deviation bounds (Hoeffding and Bernstein) on each dimension independently, and then the Empirical Likelihood method (EL-LUCB) on the joint probability vector. The effectiveness of these methods is demonstrated through simulations on scenarios with varying levels of structural complexity.

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Dates et versions

hal-04935710 , version 1 (07-02-2025)

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  • HAL Id : hal-04935710 , version 1

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Mehrasa Ahmadipour, Elise Crépon, Aurélien Garivier. Identifying the Best Transition Law. 2025. ⟨hal-04935710⟩
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